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how can i find the end behavior?

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How can i find the end behavior with these two functions?

Guest Oct 3, 2017
#1
+7401
+1

How can i find the end behavior with these two functions?

$$f(x)=\frac{-6x}{3x-5}\\ f(x)=x^2-4x-5$$

$$\frac{-6x}{3x-5}=x^2-4x-5$$

$$-6x=(x^2-4x-5)\times (3x-5)\\ -6x=3x^3-5x^2-12x^2+20x-15x+25\\ \color{blue}3x^3-17x^2+11x+25=0$$

$$x_1 \approx-.88231\\ x_2\approx 2.1443\\ x_3 \approx 4.4041\\ WOLFRAM\ |\ ALPHA$$

!

asinus  Oct 3, 2017
#2
+92933
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Mmm I do not think that is what the guest wanted asinus :)

$$f(x)=\frac{-6x}{3x-5}$$

This has an asymptote at

3x-5=0

x=5/3

lim as x tends to 5/3 from above = - infinity

lim as x tends to 5/3 from below = + infinity

As x tends to +infinity  y tends to -2

As x tends to -infinity  y tends to -2

Here is the graph.

Melody  Oct 3, 2017